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Proof step 50 from proof cast-add-2pot-h (previous step)

0 ≤ 2 ^ i + j ∧ (2 ^ i + j) % 2 ^ i ≤ 2 ^ (i - 1) - 1 ∧ 0 < i, j < 0, 0 < i, 0 < j + 2 ^ i, 0 < 2 ^ i + j, j + 2 ^ (i - 1) < 0 ⊦ (2 ^ i + j) % 2 ^ i = j + 2 ^ i

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 51:
0 ≤ i, 0 ≤ 2 ^ i + j, j < 0, 0 < i, 0 < j + 2 ^ i, 0 < 2 ^ i + j, j + 2 ^ (i - 1) < 0, (2 ^ i + j) % 2 ^ i < 2 ^ (i - 1) ⊦ (2 ^ i + j) % 2 ^ i = j + 2 ^ i

Rule argument

Additional information

Used simplifier rules: ⊦ i < 0 ∧ 0 ≤ j → i < j;% ⊦ 2 ^ (i - 1) < 2 ^ i ↔ 0 ≤ i;% ⊦ i + j < i + i0 ↔ j < i0;% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + 1 ≤ j ↔ i < j;% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;